New results of exponential synchronization of complex network with time-varying delays

Yiping Luo,Zifeng Cheng,Bifeng Zhou,Zhaoming Ling

doi:10.1186/s13662-019-1947-1

Yiping Luo, Zifeng Cheng + Show 2 more

Open Access

https://doi.org/10.1186/s13662-019-1947-1

Copy DOI

Abstract

In this study, we elucidated the exponential synchronization of a complex network system with time-varying delay. Then the exponential synchronization control of several types of complex network systems with time-varying delay under no requirements of delay derivable were explored. The dynamic behavior of a system node shows time-varying delays. Thus, to derive suitable conditions for the exponential synchronization of different complex network systems, we designed a linear feedback controller for linear coupling functions, using the Lyapunov stability theory, Razumikhin theorem, and Newton–Leibniz formula. The exponential damping rates for the exponential synchronization of different complex network systems were then estimated. Finally, we validated our conclusions through a numerical simulation.

Highlights

1 Introduction Many problems in nature can be descrobed by complex network models, such as the World Wide Web (WWW), food chains, traffic networks, and social networks
Inspired by Ref. [9], we propose a novel method to address the problems encountered in the synchronous control of a complex network with time-varying delay
4 Conclusions and discussions This work focuses on the problem of exponential synchronization in complex network systems with time-varying delay

Summary

Introduction

Many problems in nature can be descrobed by complex network models, such as the World Wide Web (WWW), food chains, traffic networks, and social networks. Synchronization is an important dynamic characteristic of a complex network. Many phenomena in nature are realized by the synchronization of complex networks. Strogatz discovered the synchronized contractions of cardiac muscle cells [1]. Steinmetz et al discovered that the attention selection modes of human beings and primates are closely related with the synchronous rates of their neurons [2]. Synchronization technologies have been widely applied in practical life. Kunbert et al suggested solving problems encountered in image processing through the use of synchronously generated autowaves [4]. Pulse, intermittent, and pinning controls have been used for the synchronous control of complex networks and thereby contributed to many outstanding works [5,6,7,8]

Objectives

Conclusion